Integrating machine learning with simultaneous quantile regression for uncertainty estimation

Abstract Accurate velocity models are crucial for understanding subsurface structures, which is vital for various subsurface activities including hydrocarbon exploration, development, and CO2 storage. The application of data-driven techniques based on machine learning (ML) to velocity model building has garnered significant attention due to their computational efficiency. However, most existing ML implementations provide only a single prediction for a given input, which may not adequately reflect the distribution of the testing data. The simultaneous quantile regression method can estimate the entire conditional distribution of the target variable given the input using pinball loss. In this study, we incorporate this technique into seismic inversion and test the proposed method on synthetic Kimberlina data. The uncertainty map is then calculated pixel by pixel from a particular prediction interval around the median. We also introduce an innovative data-augmentation method that leverages uncertainty to enhance prediction accuracy. The results validate the reliability of the calculated uncertainty in the proposed InvNet_UQ model. The method remains robust, even if the testing data are distorted due to problems in the field data acquisition. Another test demonstrates the effectiveness of the developed data-augmentation method in increasing the spatial resolution of the estimated velocity field and in reducing the prediction error.